Built under Castilian rule in the 13th and 14th centuries on the remains of a Moorish predecessor, this fort-cum-palace hosted both Fernando and Isabel, who made their first acquaintance with Columbus here in 1486. One hall displays some remarkable Roman mosaics, dug up from the Plaza de la Corredera in the 1950s. The Alcázar's terraced gardens – full of fish ponds, fountains, orange trees and flowers – are a delight to stroll around.
While you're here it's also interesting to visit the nearby Baños del Alcázar Califal , the impressive 10th-century bathhouse of the Moorish Alcázar.